Distance Formula Flashcard

Front

What is the Distance Formula?

Back

The Distance Formula is used to determine the distance between two points in a coordinate plane. It is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the distance between the points (3,-7) and (6,2)?

Back

Using the Distance Formula: d = √((6 - 3)² + (2 - (-7))²) = √(3² + 9²) = √(9 + 81) = √90 ≈ 9.5.

Front

What is the distance between -2 and 6 on a number line?

Back

The distance is calculated as |6 - (-2)| = |6 + 2| = |8| = 8.

Front

What does rounding to the nearest tenth mean?

Back

Rounding to the nearest tenth means adjusting a number to one decimal place, where the second decimal place determines whether to round up or down.

Front

How do you calculate the distance between (-10,-7) and (-8,1)?

Back

Using the Distance Formula: d = √((-8 - (-10))² + (1 - (-7))²) = √(2² + 8²) = √(4 + 64) = √68 ≈ 8.2.

Front

What is the significance of the square root in the Distance Formula?

Back

The square root is used to ensure that the distance is a non-negative value, as distance cannot be negative.

Front

What is the first step in using the Distance Formula?

Back

Identify the coordinates of the two points: (x1, y1) and (x2, y2).

Front

If the coordinates of two points are the same, what is the distance between them?

Back

The distance is 0, as there is no separation between the points.

Front

How do you interpret the result of the Distance Formula?

Back

The result represents the straight-line distance between the two points in the coordinate plane.

Front

What is the distance between the points (4,5) and (4,1)?

Back

Using the Distance Formula: d = √((4 - 4)² + (1 - 5)²) = √(0 + (-4)²) = √16 = 4.